# Fock Operator for minimization

1. Jan 19, 2012

### jusy1

Hi everyone,

I have a question about the application of the Fock operator when we want to optimize, for example, an atomic orbital written as a product of Slater Orbitals.

I know that the appeareance of the Fock operator is due to the minimization of the <E> with respect to each wavefunction, using Lagrange multipliers.

Since we do not make any assumption about the mathematical form of the orbitals we may be using, if my wavefunction had four parameters to optimize:

$$\Psi = c_1(\frac{\zeta_1^3}{\pi})^{1/2}e^{-\zeta_1r} + c_2(\frac{\zeta_2^3}{\pi})^{1/2}e^{-\zeta_2r}$$

Would I get 4 Fock equations, one for each parameter?

Because in most of the derivations of the Fock equation it's written $$dL[{\Psi_i}] = 0$$ But when we are considering an infinitesimal change on our wavefunction it can be on any of its variables: $$\frac{\partial L[{\Psi_i}]}{\partial \Psi_i}\frac{\partial \Psi_i}{\partial r_i}\partial r_i$$

Is this right?

Thank you

Last edited: Jan 19, 2012